Use the Dragon: Very early in the game after you kick down the ladder to get under the bridge easily, rest at the bonfire and climb the ladder then go up the stairs. Stand on the bridge for a second or two then go back to the bonfire and the dragon will have killed all the guys. You get 300 souls.

Soul Farming very early: For this to work you need a bow (which can be purchased from the merchant in the Undead Burg) and arrows. When you reach the point where you are underneath the bridge where the red dragon is resting you will be able to see its tail sticking out just over the right side. If you shoot the base of the tail, the dragon will do a swoop over the bridge and spray fire which will kill all those on top, which includes the skeletons, while you stay safe below. You will be awarded the souls for their deaths which amount to 300. If you jump off of the side of the underpass, climb back up the ladder from where you respawn below, and grab your souls... this process can be repeated indefinitely! It sounds like a long task but 300 souls can be earned in around 30 seconds each time. You MUST jump off of the side or die in some fashion before shooting the dragon again before it will repeat its flaming attack on the bridge again.

Soul Farming near Taurus Demon: A minor tip, after beating the Taurus Demon (I know, first you have to beat him) you'll find yourself looking at the Hellkite dragon across the span of a bridge. Run along the left side of the bridge, avoiding the arrows of the Crossbow wielding Undead, and try and make it to the far left corner of small walled area. Standing here you can avoid the fire breath of the dragon, while the enemies on the bridge will die, netting you some souls. 300, to be precise. Make your way across to the stairwell parallel to your position, descend and move across to the stairwell directly under your previous position. Here you can kick down a ladder which allows you to access the last bonfire.
Rest, proceed back up the ladder, and slowly walk over to the stairwell that led down from the surface of the bridge. If you step on the purplish stone of the bridge (just past the railing of the stairwell) the dragon will descend upon the bridge and use his fire breath, making crispy treats of all the Undead, and giving you, again, 300 souls. Just be sure to roll back down the stairwell, so. . . you know. . . you don't catch on fire. This is a great way very early on to grab some souls to grab the Heal miracle, and level up for something like the Drake Sword.